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Sagot :
144 square cm
Do the Pythagorean theorem
Since sTUV is a square one side is 13 cm
So 5^2 + x^2 = 13^2
25+ x^2 = 169
x^2 = 144
So side rv is 12 cm
Since pqrv is a square you square 12 cm and get 144 square cm for the area.
Do the Pythagorean theorem
Since sTUV is a square one side is 13 cm
So 5^2 + x^2 = 13^2
25+ x^2 = 169
x^2 = 144
So side rv is 12 cm
Since pqrv is a square you square 12 cm and get 144 square cm for the area.
Answer:
144 cm²
Step-by-step explanation:
Finding square STUV's side lengths:
Square the area of square STUV to find the side lengths.
√169 = 13
Therefore, the side lengths of square STUV are 13 cm.
Finding triangle VRS last side length:
Since we now have 2 out of 3 side lengths for triangle VRS and it's a right triangle, we can use Pythagorean Theorem to find the last leg.
a² + b² = c²
a² + 5² = 13²
a² + 25 = 169
a² = 144
√a² = √144
a = 12
Therefore, the last side length is 12 cm.
Square PQRV's area:
Now that we know the side length of square PQRV is 12 cm, simply square the value to find the area.
12² = 144
Therefore, the area of square PQRV is 144 cm².
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